But even this attempt to ensure that every New Jerseyan can cast a ballot in the wake of the worst storm in state his­tory may not be enough, election ob­servers say. They fear voters unable to ap­ply for email and fax ballots by Tuesday’s 5 p.m. deadline after technical problems in county election offices will be denied the ability to vote.

While it’s impossible to determine the exact number of voters affected, tens of thousands may be casting late ballots this year. And it’s unclear how many New Jer­seyans were unable to vote as a result of technological glitches like busy fax lines and jammed email accounts.

The move to a Friday deadline will add considerable work for county election of­ficials — who already must count paper absentee and provisional ballots cast in large numbers this year thanks to Hurri­cane Sandy. The result could be local elections that remain undecided for some time.

The Christie administration’s move to extend the deadline for some voters to cast ballots was announced Tuesday afternoon and followed a weekend of changes in the state’s election rules designed to increase ballot access. The change came as county clerks across the state were being overwhelmed by the flood of email and fax ballot requests.

“We’ve been inundated with electronic ballots,” said Robert Pantina, an aide to Bergen County Clerk John Hogan. “We have easily received over 1,000 requests either through email or fax.”

Election watchers pointed to complaints from voters contending with busy signals and overloaded email inboxes when trying to request a ballot by the 5 p.m. Election Day deadline. And they said that ballots cast after Election Day could face legal challenges.

“People are telling us that they’re not able to get through” to county clerks, said Kerry Margaret Butch, executive director of the League of Women Voters, which runs a statewide election hotline. “Their emails are getting bounced back.”

The American Civil Liberties Union of New Jersey said about 2,000 email and fax ballot requests had yet to be processed in Hudson County on Tuesday. The Essex County clerk, apparently in response to overwhelmed email systems, was telling voters to email ballot requests to his personal Hotmail account to get them in by the deadline.

The administration rolled out new email and fax voting machine procedures over the weekend for voters displaced by the storm and first responders. The option is usually available only to overseas voters and military personnel.

Voters were directed to apply for the ballots by 5 p.m. on Election Day by emailing or faxing application to their county clerks’ offices.

The move was one of several the administration made to ensure residents displaced by Sandy would have access to the polls. The state ordered expanded hours for voters to cast in-person absentee ballots at county election offices in the days preceding the election. And it permitted voters to cast provisional ballots at any polling place in the state on Election Day. County officials moved polling places from buildings damaged or left without power by the storm.

Yet it was email and fax voting procedures that appeared to cause the most problems on Tuesday.

Originally, voters had to return completed ballots to county election officials by 8 p.m. on Election Day. But a directive put out Tuesday afternoon by Lt. Gov. Kim Guadagno, the state’s top elections official, extended that time to 8 p.m. Friday. And it gave election officials until noon Friday to actually get ballots to voters.

“We simply want to ensure that New Jerseyans displaced by the storm and first responders are not disenfranchised and have access to a ballot,” said Ernest Landante, Guadagno’s spokesman, adding that the administration had done all it could to ensure a smooth voting process in chaotic conditions.

“Thousands of New Jerseyans have been displaced from their homes, while many others have lost their homes to Hurricane Sandy,” he added. “They shouldn’t lose their right to vote too.”

And the directive hasn’t assuaged concerns from election observers.

The ACLU tried, and failed, to force the state to accept federal absentee write-in ballots after polls close Tuesday for voters having trouble getting their ballot requests in by the deadline.

An Essex County Superior Court judge denied the request, which was opposed by both Democrats and Republicans, adding that state officials had promised voters whose email requests couldn’t get through because of technical glitches would still be able to vote.

“We are talking about thousands, if not tens of thousands, of voters being affected. It’s a real significant problem,” said ACLU policy counsel Alex Shalom.

Keesha Gaskins, senior counsel for the Brennan Center for Justice at New York University, said she had received reports from voters unable to submit their ballot requests.

“Attempting to apply is not the same as applying,” she said, noting that it was difficult to tell in some counties whether email or fax applications had been received.

Gaskins also said that voters may be less likely to actually return ballots received after the presidential election results are announced — possibly depressing turnout in down-ballot elections for U.S. Senate, Congress and local races.

Richard L. Hasen, a professor at the University of California, Irvine, who specializes in election law, said he was concerned that email and fax ballots cast after Election Day could be the subject of legal challenges in a close race.

“Trying to roll something out like this on the fly was an idea that was fraught with peril,” he said, adding that “there are no good solutions” to the massive challenges the state faced.

A Passaic County Superior Court judge denied a request to sequester email and fax ballots in the county received after the polls close after county Democrats questioned Guadagno’s authority to change voting rules.

County election officials, already burdened by counting scores of provisional and absentee ballots cast in large numbers by displaced voters, will have to divert resources to process ballot applications.

And the sheer volume of paper ballots could delay final vote tallies for some local races, said Eileen DiBari, Bergen County Board of Elections chairwoman.

Officials won’t be able to count the more than 35,000 mail-in ballots they received Tuesday night, she said.